SQL Server 2012 :: Window Function On Different Date Ranges?

I have a question regarding windowing functions. I have a sales order table with the columns "orderid", "customerid", "order_date" and "amount". I use the following query to get the amount of every customer as a additional column:

Select customerid,
orderid,
order_date,
amount,
SUM(amount) OVER (PARTITION BY customerid)
FROM sales_orders

My question is if there is a good way to add another column, which includes the SUM(amount) of the customerid, where the order_date > 2012-01-15 , something like this:

Select customerid,
orderid,
order_date,
amount,
SUM(amount) OVER (PARTITION BY customerid),
SUM(amount) OVER (PARTITION BY customerid WHERE order_date > 2012-01-15)
FROM sales_orders

I know, this is not a valid method, so do you know a way to achieve this? Can I maybe use CROSS APPLY or something like this? I know that I could use a subquery to get this, but is there maybe a way / a better way via window functions?